Transformations in Geometry: Rigid Motions Quiz for 8th Graders

A triangle is rotated 90 degrees clockwise around the origin. If one vertex of the triangle is at (2, 3), where will this vertex be after the rotation?

• (3, -2)

• (3, 2)

• (-3, 2)

• (2, -3)

A rectangle is reflected over the y-axis. If the original rectangle has vertices at (1, 2), (1, 5), (4, 2), and (4, 5), what are the coordinates of the vertices of the reflected rectangle?

• (1, 2), (1, 5), (4, 2), (4, 5)

• (2, 1), (5, 1), (2, 4), (5, 4)

• (-1, -2), (-1, -5), (-4, -2), (-4, -5)

• [(-1, 2), (-1, 5), (-4, 2), (-4, 5)]

A square is translated 3 units to the right and 2 units up. If one vertex of the square is at (1, 1), what are the coordinates of this vertex after the translation?

• (1, 3)

• (4, 1)

• (3, 2)

• (4, 3)

A pentagon is dilated from a point (0, 0) by a scale factor of 2. If one vertex of the pentagon is at (3, 4), where will this vertex be after the dilation?

• (3, 4)

• (4, 6)

• (6, 8)

• (1, 2)

A figure is rotated 180 degrees about the point (1, 1). If a point on the figure is at (3, 4), what will be the new coordinates of this point after the rotation?

• (4, 5)

• (2, 3)

• (-1, -2)

• (0, 0)

A triangle is translated left by 5 units and down by 3 units. If one vertex of the triangle is at (6, 7), where will this vertex be after the translation?

• (6, 4)

• (1, 7)

• (1, 4)

• (11, 10)

A quadrilateral is reflected over the line y = x. If one vertex of the quadrilateral is at (2, 3), what will be the coordinates of this vertex after the reflection?

• (2, 3)

• (4, 5)

• (3, 2)

• (1, 2)

A circle is translated 4 units to the left. If the center of the circle is at (5, 5), where will the center be after the translation?

• (5, 1)

• (0, 5)

• (4, 5)

• (1, 5)

A rectangle is rotated 270 degrees counterclockwise around its center. If one vertex is at (2, 3), what will be the new coordinates of this vertex after the rotation?

• (3, -2)

• (2, -3)

• (3, 2)

• (1, 3)

A triangle undergoes a sequence of transformations: first a reflection over the x-axis, followed by a translation 2 units up. If a vertex starts at (3, 2), what are the final coordinates of this vertex after both transformations?

• (3, 2)

• (3, 4)

• (3, 0)

• (1, 0)